This web page shows analysis results explained in more detail in article (Lavrencic, M. and Brank, B. 2018), simulating an experiment shown in (Yamaki, N. 1984).

References: Lavrencic, M. and Brank, B. (2018) Simulation of Shell Buckling by Implicit Structural Dynamics and Numerically Dissipative Schemes. Under review Yamaki, N. (1984) Elastic stability of circular cylindrical shells, Netherlands: North-Holland: p. 230/Fig. 3.52d (a), p. 433/Fig. 5.24b (i)

WOOD - BOSSAK - ZIENKIEWICZ INTEGRATION SCHEME

Shown results are for ρ_{∞}=0.6. Numerical results match well with Yamaki’s experimental results in the post-buckling area. After primary buckling, secondary buckling occurs, which is accompanied by reductions in the number of circumferential waves. The number of waves obtained by the analysis, matches with the number of waves in the experiment. The primary buckling load level depends heavily on the presence of initial imperfections.

Perfect cylinder during the analysis

Cylinder with initial imperfections during the analysis

GENERALIZED α SCHEME

Shown results were obtained using ρ_{∞}=0.8. Numerical results match well with Yamaki’s experimental results in the post-buckling area. After primary buckling, the analysis fails to catch the first postbuckling branch, but all the subsequent reductions in the number of circumferential waves are nicely captured. The number of waves obtained by the analysis, matches with the number of waves in the experiment. The primary buckling load level depends heavily on the presence of initial imperfections.

Perfect cylinder during the analysis

Cylinder with initial imperfections during the analysis

ENERGY DECAYING SCHEME

Shown results were obtained using factors α=0.02, β=0.02. Numerical results match well with Yamaki’s experimental results in the post-buckling area for the symmetric and asymmetric wave pattern. Wave oscillation after each transition is considerably smaller than for the analyses shown above.